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Cryptokyo TMUA Problem Set · Q15

ProbabilityNumber & counting

A discrete random variable XX takes non-negative values with distribution P(X=k)=ab−k\mathbb P(X=k)=ab^{-k}, where k≥0k\ge0 is an integer and a>0a>0 and b>1b>1 are real numbers.

Find aa in terms of bb.

A1b\frac1b
B1b−1\frac1{b-1}
Cbb−1\frac b{b-1}
Db−1b-1
E1−1b1-\frac1b

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